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I have a matrix, $W$, which is 500,000 x 500,000 that I need to find to optimize over the following:

$W* = argmin _{W}|| AW - B||_F^2 + \lambda || W||_1^1$

Using an iterative methods, such as gradient descent. On my local machine I can't just initialize W randomly, instead I need to create a sparse matrix and then initialize some elements. Note that W* is sparse. How to do that?

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From the scipy documentation

from scipy.sparse import rand
matrix = rand(500000, 500000, density=0.25, format="csr", random_state=42)

You can use the parameter density to choose how dense you want your matrix:

density equal to one means a full matrix, density of 0 means a matrix with no non-zero items.

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  • $\begingroup$ wouldn't that effect the optimization performance though? $\endgroup$
    – rando
    Nov 14, 2020 at 0:42
  • $\begingroup$ In which sense? Did I answer the question on how "to create a sparse matrix and then initialize some elements"? Have you tried it? $\endgroup$
    – Ale
    Nov 14, 2020 at 10:47

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